Figure 1.
Variation in hub avPCC distribution.
Probability density plots of the distribution of hub avPCC values for human interaction data from OPHID (provided by Taylor et al. [2]). Gene expression data from GeneAtlas [43], normalised using (a) MAS5 and (b) GCRMA [42]. Curves obtained using a normal smoothing kernel function at varying window widths. Hartigan's DIP test for unimodality [16], [17] returns values of 0.0087 (-value
) for (a) and 0.0062 (
-value
) for (b), indicating no significant deviation from unimodality in either case.
Figure 2.
Effects of hub deletion on network connectivity.
(a) FYI network [1]. ‘Date (−SPC24)’ refers to the set of date hubs minus the protein SPC24. In each case, we used the complete network consisting of 1379 nodes as the starting point and then deleted all hubs in the given set from the network in order of decreasing degree. The characteristic path length is the mean of the lengths of all finite paths between two nodes in the network. (b) FHC network [4]. ‘Date (−high BC)’ refers to the set of date hubs minus the 10 hubs with the highest betweenness centrality (BC) values (listed in Table 1). We used the upper bound on the BC for party hubs as a threshold to define these 10 ‘high BC’ date hubs. (Note: Results similar to those presented here are obtained if the hubs are divided into bottleneck/non-bottleneck categories [7] instead of date/party categories.)
Table 1.
High-betweenness hubs in the FHC network.
Figure 3.
Topological node role assignments and relation with avPCC.
Plots for (a) Yeast network (FHC [4]—2,233 nodes, 63 communities) and (b) Human network (CCSB-HI1 [49]—1,307 nodes, 38 communities) (see Materials and Methods for details). Following Guimerà and Amaral [31], we designate the roles as follows: R1 – Ultra-peripheral; R2 – Peripheral; R3 – Non-hub connector; R4 – Non-hub kinless; R5 – Provincial hub; R6 – Connector hub; and R7 – Kinless hub. We colour proteins according to the avPCC of expression with their interaction partners. We computed expression avPCC using the stress response data set [40] (which was the largest, by a considerable margin, of the expression data sets used in the original study [1]) for FHC and COXPRESdb [67] for CCSB-HI1. No partner expression data was available for a few proteins (25 in FHC, 1 in CCSB-HI1)—these are not shown on the plots.
Figure 4.
Rolewise hub avPCC distributions.
Plots show node role versus average expression correlation with partners for hubs in yeast (FHC [4]—553 hubs with a minimum degree of 7) and human (CCSB-HI1 [49]—326 hubs with a minimum degree of 4) networks. Larger circles represent means over all nodes in a given role. Note that ‘hub’ as used in the role names refers only to within-community hubs, but all of the depicted nodes are hubs in the sense that they have high degree. In each case, we determined the degree threshold so that approximately the top 20% highest-degree nodes are considered to be hubs. We also fixed the date/party avPCC threshold at 0.5, in accordance with Bertin et al. [4].
Table 2.
Protein interaction data sets.
Table 3.
Comparisons of yeast data sets.
Figure 5.
Relating interaction betweenness, co-expression, and functional similarity.
Plots show link betweenness centralities versus expression correlations, with points coloured according to average similarity of interactors' GO (Cellular Component) annotations, for two protein interaction data sets: FYI [1] (778 nodes, 1,798 links) and FHC [4] (2,233 nodes, 5,750 links). PCC values of log(link betweenness) with functional similarity are (
-score
,
-value
) for FYI,
(
-score
,
-value
) for FHC.